A framework for discrete valuations in Sage

[saraedum]

Based on the sage package https://github.com/mclf/mac_lane.

Depends on #21782
Depends on #23166
Depends on #23167
Depends on #21879
Depends on #23185
Depends on #23203
Depends on #23204
Depends on #23211
Depends on #23188
Depends on #21879
Depends on #23186
Depends on #23191
Depends on #21996
Depends on #23190
Depends on #23495
Depends on #23483
Depends on #23510
Depends on #23525
Depends on #23620
Depends on #23642
Depends on #23965
Depends on #23966

Component: commutative algebra

Keywords: discrete valuations, valuations, function fields, smooth projective curves, Mac Lane algorithm, Montes algorithm, sd87

Author: Julian Rüth

Branch: 24807e3

Reviewer: GaYee Park, Stefan Wewers, David Roe, Padmavathi Srinivasan, Shiva Chidambaram

Issue created by migration from https://trac.sagemath.org/ticket/21869

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

e01a3ab

Require incomparability

[saraedum]

comment:294

The changes could make some outputs gain precision. Let's see what the patchbots think…

[roed314]

comment:295

There's an extra space in the new commit: 10*x^1 2.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2142891

fix copy & paste mistake

[sagetrac-git]

Changed commit from e01a3ab to 2142891

[roed314]

comment:297

I'm trying to build the documentation now to check the previous change.

---

New commits:

2142891

fix copy & paste mistake

[saraedum]

comment:298

File "src/sage/rings/padics/padic_valuation.py", line 726, in sage.rings.padics.padic_valuation.pAdicValuation_base.extensions
Failed example:
    QQ.valuation(2).extensions(L)
Expected:
    Traceback (most recent call last):
    ...
    ValueError: The valuation [ Gauss valuation induced by 2-adic valuation, v(x) = 1/2 ] does not approximate a unique extension of 2-adic valuation with respect to x^4 + 2*x^3 + 2*x^2 + 8
Got:
    [[ 2-adic valuation, v(x + 2) = 3/2 ]-adic valuation,
     [ 2-adic valuation, v(x) = 1/2 ]-adic valuation]

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

963ceb7	Fix incorrect doctest output
4900f56	Merge branch 'u/saraedum/a_framework_for_discrete_valuations_in_sage' of git://trac.sagemath.org/sage into t/21869/a_framework_for_discrete_valuations_in_sage

[sagetrac-git]

Changed commit from 2142891 to 4900f56

[sagetrac-git]

Changed commit from 4900f56 to 24807e3

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

24807e3

Merge remote-tracking branch 'trac/develop' into t/21869/a_framework_for_discrete_valuations_in_sage

[roed314]

comment:303

The failing builds look to be due to some unrelated giac issue, and I don't know what the failed apply is. I'm happy with the changes and the documentation builds when I test it. Let's set this back to positive review.

[vbraun]

Changed branch from u/saraedum/a_framework_for_discrete_valuations_in_sage to 24807e3

[saraedum]

Changed commit from 24807e3 to none

[jdemeyer]

comment:306

What's the point of these doctests?

        Note that this does not affect comparison of valuations which do not
        coerce into a common parent. This is by design in Sage, see
        :meth:`sage.structure.element.Element.__richcmp__`. When the valuations
        do not coerce into a common parent, a rather random comparison of
        ``id`` happens::

            sage: w = valuations.TrivialValuation(GF(2))
            sage: w <= v # random output
            True
            sage: v <= w # random output
            False

I plan to remove them in #26934

[saraedum]

comment:307

I thought that the docstring is quite technical, so the doctest illustrates what I mean. They don't "test" anything, they are really part of the documentation.

[jdemeyer]

comment:308

Replying to @saraedum:

I thought that the docstring is quite technical, so the doctest illustrates what I mean.

I see your point, but it's not the job of valuation.py to document technical details of the coercion model. I ask because I plan to change the behaviour of comparisons in #22029.

[saraedum]

comment:309

It's a detail of the coercion model but here the point is just that it does not work the way you would expect it to. Comparisons are important in this context and it's therefore important to document the limitations. If it raises an error, all the better.